I use the sterile stuff. I don't buy organic to make a statement. Mostly the inverse statement of everyone who buys everything organic! But as far as sterile cotton, this is usually how it's done.
Medical products must be sterilized in the container in which they are sold. This is why the sterile cotton from CVS comes in a paper bag. Sterile cotton is first sorted and processed to make sure no contaminants are in the product. A wound dressing would not work well if it has twigs and other junk that is found in the field where it is grown. This process ensures that the sterile cotton is more "pure" than the organic has to be to be sold commercially. The cotton is then treated with a hydrogen peroxide solution and packaged wet in the inner paper container. It is then heated to a temperature that is high enough to kill microorganisms without igniting the cotton (which is wet, so it can be heated to higher temperatures). The end result is sealed sterile cotton.
A bunch of people have been concerned about residual hydrogen peroxide in the cotton when it is used for vaping. This is essentially a non-issue. In order for anything to bear the "U.S.P." title it must conform to standards for impurity, which include any remaining hydrogen peroxide. When hydrogen peroxide (H2O2) is exposed to organic material or heat it decomposes to a mix (depending on the steps of the reaction) of hydrogen, water, and oxygen. This is then removed by the heat in the sterilization process. Hydrogen peroxide is unstable on it's own, which is why a bottle of H2O2 becomes less effective after it's past it's expiration date.
In short, the sterile cotton actually has less contaminants than the organic cotton. "Organic" does NOT mean pesticide free, and there is no real data to show how well boiling actually removes these contaminants. Most organic fertilizers and pesticides contain metals, which are exactly some of the things people are concerned about inhaling. Personally I would stay with the sterile cotton and avoid the organic.